My take:
Computer Engineering

Why? I went into Electrical Engineering with a emphasis on computing systems as a result I took almost as many CS courses as EE courses. I really enjoyed the CS courses; but the reality is that I would have never considered CS because it's basically a degree of washouts. IE people that can't handle the Engineering courses wash out into CS, Business, or Economics majors. That said; I did graduate in 96 so... times may have changed. Even back then; the CS majors were almost 95% Indian transfer students.

I graduated in 96... did a year at AMAT working on computer chip fab equipment then immediately got a job working for the leading CPU manufacturer with a site in Hillsboro, OR. I've been working for them for 23 years. I've held a handful of positions at this employer and have enjoyed the jobs for the most part. I've almost always gravitated toward the software roles... because I have the right logical mind to debug those systems. At the moment; I hold the title of SR Firmware Engineer so I interact with the CPU and the software which runs it (UEFI).

If I were to do it over again; I'd probably still get a BSEE... but minor in CS instead of math. I hated advanced math classes... and still do. If your son can't make it as an EE; then he could transfer to the CS college without loosing a lot of credits.

That's called School of Hard Knocks.
My first PC was built out of the back of a Computer Shopper back in 1990 and it didn't even have a hard drive at the time. That will put hair on your "computer" chest. That "event" eventually led me to a job with a dropped E in Hillsboro.

Never be afraid to figure stuff out on your own.

Did you send him to the manager of a Grocery store via a pinkslip?
Cause yeah; umm... that's bad.